Space of modular forms of level 1332, weight 2, and Character 1332.q

• Label: 1332.2.q
• Level: $1332$
• Weight: $2$
• Character orbit: 1332.q
• Rep. character: $\chi_{1332}(529,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $76$
• Newform subspaces: $1$
• Sturm bound: $456$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1332 = 2^{2} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1332.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 333 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(456\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1332, [\chi])\).

	Total	New	Old
Modular forms	468	76	392
Cusp forms	444	76	368
Eisenstein series	24	0	24

Trace form

76 * q - 2 * q^3 + q^7 + 2 * q^9 - 4 * q^11 + 3 * q^15 - 3 * q^21 - 6 * q^23 - 64 * q^25 - 23 * q^27 - 9 * q^29 + 6 * q^31 + 16 * q^33 - 18 * q^35 - 5 * q^37 - 12 * q^39 + 12 * q^41 + 6 * q^43 + 3 * q^45 - 2 * q^47 - 39 * q^49 - 18 * q^51 + 14 * q^53 + 42 * q^57 + 3 * q^59 + 37 * q^63 + 32 * q^65 - 20 * q^67 - 3 * q^69 - 13 * q^71 - 14 * q^73 + 3 * q^75 + 36 * q^77 - 3 * q^79 + 14 * q^81 - 34 * q^83 - 12 * q^85 - 6 * q^87 - 30 * q^89 - 21 * q^91 + 6 * q^93 + 22 * q^95 - 48 * q^97 + 44 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1332, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1332.2.q.a	$1332$	$2$	1332.q	333.k	$6$	$76$	$38$	$10.636$		None		✓	✓	✓	1332.2.q.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(1\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1332, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1332, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(666, [\chi])\)\(^{\oplus 2}\)